The Mirror reports that Astori was on the shopping list before Dejan Lovren joined the Saints in January.
The 26-year-old has also been strongly linked with the likes of AC Milan and Everton.
The £10million-rated defender played for Italy in the Confederations Cup in Brazil last summer.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?